NS, composed by a conservative continuity equation . If the flow is incompressible, id est if the variations
of the density of the fluid do not have appreciable effects, the density can be considered with a good approximation, a constant.
And a non-conservative Momentum equation
not exactly measurable as a scalar field, but non-linear, divisible by
3 scalar equations laid and projected along the directions x, y, z .

So we have 4 independent variables x,y,x,t and the 4 dependent variables u,v,w, (velocity components)
and p (pressure) and 6 other dependente variables given by the Stress Tensor:

Then , considering the components of the viscous stress state are linearly linked
to the components of the deformation velocity through Stokes' relations , we have :

whereas

so we saw this tensor as a generally irregular pyramid with triangular base ,
but if we consider it as a deformable and curvable sheet, we may have a new vision about these equations

The Metric Tensor g expresses the property of a geometrically curvable structure
with the points of its lattice at a distance
always equal in relation to the structural components themselves:

= distance of point from origin, whatever the inclination of the reference axes =
(using the Einstein notation)
where

then then then

contravariant metric tensor: , covariant metric tensor:

so we can maintain the position of the points created in the cube, transferring them to a deformable sheet

2-dimensional viscous stress tensor :

hence, the 10 dependent variables can be reduced to 6 ,
while the equations used to give them a solution are 3 , hence the difference is reduced from 6 to 3 :

Continuity:

Momentum:

where
= metric abscissa
= metric ordinate

hence we can calculate the amount of energy created over a certain period of time by these simplified
new version of N-S equations:

but this is not enough to overcome the non-linearity. We need an output unidimensional parameter.
Then we examine a lagrangian particle that in its path creates a String.
Nambu-Goto equation analyzes the behavior of the string and the energy produced by it,
proportional to the minimum area of the worldsheet area. So we apply the N-G's Action : where